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Full text of "IS 14673: Liquid flow measurement in open channels by weirs and flumes - Triangular profile weirs"

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IS 14673 (1999) : Liquid flow measurement in open channels 
by weirs and flumes - Triangular profile weirs [WRD 1: 
Hydrometry] 




Jawaharlal Nehru 
'Step Out From the Old to the New" 



aj^&vi iJii^s:y%K^ isb^^ni^seg 



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K^^^iXSVCd^ 



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Invent a New India Using Knowledge 



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^'^^^r 



k 




BLANK PAGE 



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PROTECTED BY COPYRIGHT 



IS 14673 : 1999 

( Reaffirmed 2004 ) 



Indian Standard 

LIQUID FLOW MEASUREMENT IN OPEN CHANNELS 

BY WEIRS AND FLUMES — TRIANGULAR 

PROFILE WEIRS 



ICS 17.120.0 



© BIS 1999 

BUREAU OF INDIAN STANDARDS 

MANAK BHAVAN, 9 BAHADUR SHAH ZAFAR MARG 
NEW DELHIl 10002 



May 1999 Price Group 6 



Fluid Flow Measurement Sectional Committee, RVD 1 



FOREWORD 

This Indianiltandard was adopted by the Bureau of Indian Standards, after iSxe draft finalized by the Fluid Flow 
Measurem^t Sectional Committee had been approved by the River Valley Division Council 

Various methods are adopted for measurement of flow of water in open channels like velocity area method, 
slope area method, etc, depending upon the channel, flow conditions, measuring equipment etc* Triangular 
profile weirs are used for flow measurement in open channels under steady flow conditions. This Indian Standard 
on liquid flow measurement by triangular profile weirs has been prepared based on ISO 4360 : 1984 'Liquid 
flow measurement in open channels by weirs and flumes — Triangular profile weirs' and, therefore, is technically 
equivalent to the ISO Standard. 

For measurem-ent of uncertainties reference shall be m.ade to ISO 5168 : 1978 'Measurem-ent of fluid flow — 
Estimation of uncertainty of a flow rate measurement', since corresponding Indian Standard on the subject is 
not available as yet. 

For the purpose of deciding whether a particular requirement of this standard is complied with, the final value, 
observed or calculated, expressing the result of a test or analysis, shall be rounded off in accordance with 
IS 2 : 1960 'Rules for rounding off numerical values (revised)\ The number of significant places retained in 
the rounded off value should be the same as that of the specifled value in this standard. 



IS 14673 : 1999 



Indian Standard 



LIQUID FLOW MEASUREMENT IN OPEN CHANNELS 
BY WEIRS AND FLUMES — TRIANGULAR 



nT^/^T7TT "n Tirr7TrkCi 



1 SCOPE 

This standard specifies methods for the measurement 
of the flow of water in open channels under steady 
flow conditions using triangular proflle weirs. The 
flow conditions considered are steady flows which are 
uniquely dependent on the upstreair* head and drowned 
flows which depend on downstream as well as 
upstream, levels. 

2 REFERENCES 

The following standards contain provisions which 

this standard. At the time of publication the editions 
indicated were valid. All standards are subject to 
revision, and parties to agreements based on this 
standard are encouraged to investigate the possibility 
of applying the most recent editions of the standards 
indicated below: 

IS No. Title 

1191 : 1971 Glossary of termiS and symbols used 

in connection with the measurement 
of liquid flow with a free surface 
{first revision) 

1 192 : 1981 Velocity area methods for measure- 

ment of flow of water in open 
channels (first revision) 
9116 : 1979 Specification for water stage recorder 
(float type) 

3 DEFINITIONS AND SYMBOLS 

For the purpose of this Indian Standard, the definitions 
given in IS 1191 shall apply. The symbols used in this 
Indian Standard are given in Annex A. 

4 UNiTS OF MEASUREMENT 

The units of measurement used by this standard are 
seconds and metres. 

5 INSTALLATION 

Conditions regarding preliminary survey, selection of 
site, installation, the approach channel, maintenance, 
measurement of head, and stilhng or float wells which 
are generally necessary for flow measurement are given 
in the following sub-clauses. The particular 
requirements for the triangular profiles weirs are given 
separately in 8. 



5.1 Selection of Site 

5.1.1 A preliminary survey shall be made of the 
physical and hydraulic features of the proposed site, 
to check that it conforms (or may be made to conform) 
to the requirements necessary for measurement by a 
weir. 

5.1.2 Particular attention should be paid to the 
following features in selecting the site: 



—/ 

^} 
c) 
d) 

e) 



AvailnHilitv rvf nn nHf^niiatp IpnatVi nf ph5ln- 
nel of regular cross section; 



J- liV VA.i:3VLll^ ...... 






The avoidance of a steep channel, if possible; 
The effects of any increased upstream water 
level due to the measuring structure; 
Conditions downstream including such in- 
fluences as tides, confluences with other 
streams, sluice gates, miiidams and other 
controlling features which might cause sub- 
merged flows; 

The impermeability of the ground on which 
the structure is to be founded, and the neces- 
sity for piling, grouting or other sealing-in 
river installations; 

The necessity for flood banks to confine the 
maximum discharge to the channel; 
The stability of the banks and the necessity 
for trimming and/or revetment in natural 
channels; 

The clearance of rocks or boulders from the 
bed of the approach channel; and 
The effect of wind; wind can have a consid- 
erable effect on the flow in a river or over a 
weir, especially when these are wide and the 
head is small and wheathe prevailing wind 
is in a transverse direction. 



necessary for satisfactory measurement, the site shall 
be rc'ected unless suitable im^rovem.cnts are 
practicable, 

5.1.4 If an inspection of the stream shows that the 
existing velocity distribution is regular, then it may 
be assumed that the velocity distribution will remain 
satisfactory after the construction of a weir. 



g) 

h) 

J) 
k) 



IS 14673 : 1999 



5.1.5 If the existing velocity distribution is irregular 
and no other site for a gauge is feasible, due 
consideration shall be given to checking the 
distribution after the installation of the weir and to 
improving it if necessary. 

5J.6 Several methods are available for obtaining a 
more precise indication of irregular velocity 
distribution: Velocity rods, floats or concentrations of 
dye can be used in small channels, the latter being 
useful in checking conditions at the bottom of the 
channel. A complete and quantitative assessment of 
velocity distribution may be made by means of a 
current meter. Complete information about the use of 
current meters is given in IS 1 192. 

5.2 Installation Conditions 

5.2.1 General 

The complete measuring installation consists of an 
approach channel, a measuring structure and a 
downstream channel. The conditions of each of these 
three components affect the overall accuracy of the 
measurements. 

Installation requirements include such features as weir 
finish, cross-sectional shape of channel, channel 
roughness, influence of control device, upstream or 
downstream of the gauging structure. 

The distribution and direction of velocity, determined 
by the features outlined in 5. LI have an important 
influence on the performance of the weir. 

Once an installation has been constructed, the user 
shall prevent any change which could affect the 
discharge characteristics. 

5.2.2 Approach Channel 

On all installations the flow in the approach channel 
shall be smooth, free from disturbance and shall have 
a velocity distribution as normal as possible over the 
cross-sectional area. This can usually be verified by 
inspection or measurement. In the case of natural 
streams or rivers this can only be attained by having a 
long straight approach channel free from projections 
either at the side or on the bottom. Unless otherwise 
specified in the appropriate clauses, the following 
general requirements shall be complied with: 

a) The altered flow-conditions due to the con- 
struction of the weir might have the effect of 
building up shoals of debris upstream of the 
structure, which in time might effect the flow 
conditions. The likely consequential changes 
in the water level shall be taken into account 
in the design of gauging stations. 

b) In an artificial channel the cross -section shall 
be uniform and the channel shall be straight 



for a length equal to at least five times its 
breadth. 

c) In a natural stream or river the cross-section 
shall be reasonably uniform and the channel 
shall be straight for such a length as to 
ensure regular velocity distribution. 

d) If the entry of the approach channel is through 
a bend or if the flow is discharged into the 
channel through a conduit of smaller cross- 
section, or at an angle, then a longer length of 
straight approach channel may be required to 
achieve a regular velocity distribution. 

e) There shall be no baffle nearer to the points 
of measurement than five times the maximum 
head to be measured. 

f) Under certain conditions, a standing wave 
may occur upstream of the gauging device, 
for example, if the approach channel is steep. 
Provided this wave is ^t a distance of not less 
than 30 times the maximum head upstream, 
flow measurement will be feasible, subject to 
confirmation that a regular velocity distribu- 
tion exists at the gauging station. 

5.2.3 Measuring Structure 

The structure shall be rigid and watertight and capable 
of withstanding flood flow conditions without 
distortion and fracture. It shall be at right angles to 
the direction of flow and shall conform to the 
dimensions given in the relevant clauses. 

5.2.4 Downstream of the Structure 

The channel downstream of the structure is of no 
importance as such if the weir has been so designed 
that the flow is modular under all operating conditions. 
A downstream gauge shall be provided to measure 
tailwater levels to determine when submerged flow 
occurs. 

In the event of the possibility of scouring downstream 
which phenomenon may also lead to the instability of 
the structure, particular measure to prevent this 
happening may be necessary. 

A crest tapping and separate stilling well shall be fitted 
if the weir is designed to operate in a drowned 
condition or if there is a possibility that the weir may 
drown in the future. 

The latter circumstances may arise if the altered flow 
conditions due to the construction of the weir have 
the effect of building up shoals of debris immediately 
downstream of the structure or if river works are 
carried out downstream at a later date. 

6 MAINTENANCE 

Maintenance of the measuring structure and the 



IS 14673 : 1999 



approach channel is important to secure accurate 
continuous measurements. 

It is essential that the approach channel to weirs should 
be kept clean and free from silt and vegetation as far 
as practicable for at least the distance specified in 5.2.2. 
The float well and the entry from the approach channel 
shall also be kept clean and free from deposits. 

The weir structure shall be kept clean and free from 
clinging debris and care shall be taken in the process 
of cleaning to avoid damage to the weir crest. 

7 MEASUREMENT OF HEAD 

7.1 General 

The head upstream of the measuring structure may be 
measured by a hook-gauge, point-gauge or staff-gauge 
where spot measurements are required, or by a 
recording-gauge where a continuous record is required, 
and in many cases it is preferable to measure heads in 
a separate stilling-well to reduce the effects of water 
surface irregularities. 

The discharges given by the working equation are 
volumetric figures, and the liquid density does not 
affect the volumetric discharge for a given head 
provided that the operative head is gauged in liquid 
of identical density. If the gauging is carried out in a 
separate well, a correction for the difference in density 
may be necessary if the temperature in the well is 
significantly different from that of the flowing liquid. 
However, it is assumed herein that the densities are 
equal. 

7.2 StilHng-Well or Float-Well 

Where provided, the stilling-well shall be vertical and 
have a free-board of 0.6 over the maximum water level 
estimate to be recorded in the well. 

It shall be connected to the river by an inlet pipe or 
slot, large enough to permit the water in the well to 
follow the rise and fall of head without significant 
delay. 

The connecting pipe or slot shall, however, be as small 
as possible, consistent with ease of maintenance, or, 
alternatively, shall be fitted with a constriction to damp 
out oscillations due to short amplitude waves. 

The well and the connecting pipe or slot shall be 
watertight where provided for the accommodation of 
the float of a level recorder, the well shall be of 
adequate diameter and depth to accommodate the float. 

The well shall also be deep enough to accommodate 
any silt which may enter, without the float grounding. 
The float-well arrangement may include an 
intermediate chamber between the stilling-well and 



the approach channel of similar proportions to the 
stilling-well to enable silt and other solids to settle 
out. For case of maintenance the pipework may be 
valved. 

For detailed description of the stilling-well (see 
IS 91 16). 

7.3 Zero Setting 

A means of checking the zero setting of the head- 
measuring devices shall be provided, consisting of a 
datum related to the level of the weir. 

A zero check based on the level of the water when the 
flow ceases is liable to serious errors from surface 
tension effects and shall not be used. 

As the size of the weir and the head on it reduces, 
small errors in construction and in the zero setting 
and reading of the head-measuring device become of 
greater importance. 

8 SPECIFICATION FOR THE STANDARD WEIR 

8.1 Description 

8.1.1 The weir comprises an upstream slope of 
1 (vertical) to 2 (horizontal) and a downstream slope 
of 1 (vertical) to 5 (horizontal). The intersection of 
these two surfaces forms a straight line crest, 
horizontal and at right angles to the direction of flow 
in the approach channel. Particular attention shall be 
given to the crest itself, which shall possess a well- 
defined comer of durable construction. The crest may 
be made of pre-formed sections, carefully aligned and 
jointed, or may have a non-corrodible metal insert, as 
an alternative to in-situ construction throughout. 

8.1.2 The dimensions of the weir and its abutments 
shall conform to the requirements indicated in Fig. 1 . 
Weir blocks may be truncated but not so much as to 
reduce their dimensions in plan to less than 1 .0 h^^^ 
for the 1 : 2 slope and 2.0 h^^ for the 1 : 5 slope. 

8.2 Location of Head Measurement Section 

Piezometers or point-gauge stations for the 
measurement of head on the weir shall be located at a 
sufficient distance upstream from the weir to avoid 
the region of surface drawdown. On the other hand, 
they shall be close enough to the weir to ensure that 
the energy loss between the section of measurement 
and the control section on the weir shall be negligible, 
it is recommended that the head-measurement section 
shall be located at a distance equal to twice the 
maximum head (2 h^^J upsteam of the crest. 

8.3 Condition for Modular Flow 

8.3.1 Flow is modular when it is independent of 



IS 14673 : 1999 



UPSTREAM HEAD 



STILLING WELLS 



CREST TAPPING HEAO 




''^^'i:^ 



'^'^^^^ 



Fig. 1 Triangular Profile Weir 



variations in tailwater level. This requirement is met 
when the tailwater total head above crest level is equal 
to or less than 75 percent of the upstream total ihead 
above crest level. 

8.3.2 A significant error in the calculated discharge 
will develop if this ratio is exceeded, unless a crest 
tapping is provided and two independent head 
measurements are made. 

8.4 Location of Crest Tapping 

8.4.1 The crest tapping shall consist of five to ten 
holes of 10 mm diameter drilled in the weir block 
with centres 75 mm apart, 20 mm down from the 
weir crest on the 1 : 5 slope. Alternatively pipes 
may be installed during construction. The edges of 
the holes shall not be rounded or burred. The 
number of holes shall be sufficient to ensure that 
the water level in the stilling-well follows variations 
in crest separation pocket pressure without 
significant delay. 

8.4.2 The optimum position for the crest tapping is at 
the centre of the weir crest. The tapping may be off- 
centre on weirs wider than 2,0 m provided that the 
distance from the centrehne of the crest tapping to 
the nearest side wall or pier is greater than 1.0 m. 



9 DISCHARGE CHARACTERISTICS 

9.1 Equations 

9.1.1 The discharge equation for modular flow is: 

where 

Q - the discharge over the weir, in cubic 
metres per second; 

C^ = the coefficient of discharge (non-dimen- 
sional); 

C^ ^ the coefficeint allowing for the effect of 



approach velocity 



H 



3/2 



(non- 



dimensional); 
H = the total head, in metres; 
h ^ the breadth of the weir, in metres; 
g ~ the acceleration due to gravity, in metres 

per second squared; and 
h ^ the measured head, in metres. 
9.1.2 The discharge equation for drowned flow is; 



vV'2 



.3/2 



where /is the drowned flow reduction factor (non- 
dimensional). 



9.2 Coefficients 

9.2.1 The coefficient C^ for the modular flow equation 
is obtained from Fig. 2 where A is the area of the 
approach channel. 

9.2.2 The combined coefficient C^for the drowned 
flow equation is obtained from Fig. 3 where h is the 
measured crest tapping head above crest level. Under 
modular flow conditions, the value of h Ih is constant 
at 0.20 and the value of/is 1.00. Hence, under these 
conditions, values of CJ read from Fig. 3 coincide 
with values of C^ from Fig. 2. 

9.2.3 For water at ordinary temperatures C^ is almost 
independent of /i, except at very low heads when fluid 
properties influence the coefficient. C^ is given by the 
following equation: 



Q = 1.163 



1- 



0.000 3 



x3/2 



where hh in metres. For practical purposes, C^ can 
be set equal to 1.163 for h > 0.1 m, 

9.3 Limitations 

The following general limitations are recommended: 

h > 0,03 m (for a crest section of smooth metal 

or equivalent); 
h > 0,06 m (for a crest section of fine 













IS 14673 


1999 




P 
b 

h/p 
b/h 


> 
> 

< 
> 


concrete or 
0.06 m; 
0.3 m; 
3.5; and 
2.0. 


equivalent); 






9.4 


Accuracy 









9.4.1 The relative accuracy of flow measurements 
made with these, weirs depends on the accuracy of the 
head measurement, the measurements of dimensions 
of the weir and on the accuracy of the coefficients as 
they apply to the weir in use. 

9.4.2 With reasonable care and skill in the construction 
and installation of a triangular profile weir, the 
percentage systematic error in the coefficient of 
discharge (including C^ and J) may be deduced from 
the equation: 



X\ = ± 



IOC, 
/ 



-9 



Numerical values of^'^ are given in Table 1. 

The random error depends on the quality of the 
research used to determine the coefficient and may be 
taken as A^ = ± 0.5 percent in this case. 

9,4.3 The method by which the errors in the 
coefficients are to be combined with other sources of 
errors is given in 10. 



.„0-25 0-30 0-35 


0.40 045 0&. 


V25 


T 




: I 




ji 




T 




: z 


>zo 


J 




r 




: z 




. 7 


4 JC , f^ 


\ jL -* 


-it 




'^A 




Tcf^ - 




(y^U - 




110 V^^ 




1-10 K^ 




y 




^^ 




^^ 




.j.^^ 




1-05 


~ 1 ' .M-i.O'^''.^--'" 




7ac,<''''^.rr - 




\\%l^^ 


.— •— — - 


"tT^ 


■tftri — ■.^— a== 1 1 H— I 1 — L 





OOO O'OS 0-10 0-1S 0-20 

Fk;. 2 CoHFFiciHNT OF Afhroach VnLocn y, C 



0^25 



■c -c 




Fig. 3 Drowned Flow — C /"in Terms of — and — ,/— C — 

h 3 V3 " ^ 



IS 14673 : 1999 



IOC, 
Table 1 Values of ^\ as a Percentage, in Terms of C^ and/ ^"c = ±1 — r^ - 9 



/ 



(Clause 9.4.2) 



n*oi 


fAA Af GimKn*Ak*A 




Coefncient of Approach Velocity Cy 




1.00 


1.05 


1.10 


1.15 


1.20 


1.25 










2/3 


>^G 


bhxih 






/ 


hA 


h^x 


0.00 


0.24 


0.33 


0.38 


0.42 


0.45 


1.00 


< 0.69 


< 0.20 


1.00 


1.50 


2.00 


2.50 


3.00 


3.50 


0.95 


0,86 


0.39 


1.53 


2.05 


2.58 


3.11 


3.63 


4.16 


0.90 


0.92 


0.52 


2.11 


2.67 


3.22 


3.78 


4,33 


4.89 


0.85 


0.93 


0.62 


2.76 


3.35 


3.94 


4.53 


5.12 


5.71 


0.80 


0.94 


0.70 


3.50 


4.13 


4.75 


5.38 


6.00 


6.63 


0.75 


0.94 


0.76 


4.33 


5.00 


5.67 


6.33 


7.00 


7.67 


0.70 


0.95 


0.81 


5.29 


6.00 


6.71 


7.43 


8.14 


8.86 


0.65 


0.96 


0.85 


6.38 


7.15 


7,92 


8.69 


9.46 


10.23 


0.60 


0.96 


0.88 


7.67 


8.50 


9.33 


10,17 


11.00 


11,83 


0.55 


0.97 


0.91 


9.18 


10.09 


11,00 


11.91 


12.82 


13.73 


0.50 


0.97 


0.92 


11.00 


12,00 


13.00 


14.00 


15.00 


16.00 



9.4,4 In general, calibration experiments have been 
carried otkt on model structures of small dimensions 
and when transferred to larger structures there may 
be small changes in the discharge coefficients due to 
scale effects. 

10 UNCERTAINTIES IN FLOW MEASUREMENT 

10.1 General 

10.1.1 Reference should be made to ISO 5168. 

10.1.2 The total uncertainty of any flow measurement 
can be estimated if the uncertainties from various 
sources are combined. In general, these contributions 
to the total uncertainty may be assessed and will 
indicate whether the rate of flow can be measured with 
sufficient accuracy for the purpose in hand. This clause 
is intended to provide sufficient information for the 
user of this standard to estimate the uncertainty in a 
measurement of discharge. 

10.1.3 The eiTor may be defined as the difference 
between the true rate of flow and that calculated in 
accordance with the equation used for calibrating the 
measuring structure, which is assumed to be 
constructed and installed in accordance with this 
standard. The term ^uncertainty' is used here to denote 
the range within which the true value of the measured 
flow is expected to lie some ninteen times out of twenty 
(95 percent confidence limits). 

10.2 Sources of Error 

10.2.1 The sources of error in the discharge 
measurement may be identified by considering a 
generalized form of discharge equation for weirs: 



e-(2/3) 



^n 



Q Csfss 



bh 



3/2 



where 

(2/3)^^^ == a numerical constant not subject to 
error; and 

g == the acceleration due to gravity, 

varying from place to place, but the 
variation is small enough to be 
neglected in flow measurement. 

10.2.2 The sources of error which need to be considered 
further are: 

a) the discharge coefficient Q the velocity of 
approach coefficient C^. and the drowned flow 
reduction factor/ Numerical estimates and 
uncertainties in the combined coefficient 
CjCy are given in 9.4; 

b) the dimensional measurement of the struc- 
tures, for example the breadth of the weir, b\ 
and 

c) The measured head, /i. 

10.2.3 The uncertainties in b and h shall be estimated 
by the user. The uncertainty in dimensional 
measurement will depend upon the accuracy to which 
the device as constructed can be measured: in practice, 
this error may prove to be insignificant in comparison 
with other errors. The uncertainty in the head will 
depend upon the accuracy of the head-measuring 
device, the determination of the gauge zero and upon 
the technique used. The error may be small if a vernier 
or micrometer instrument is used, with a zero 
determination of comparable precision. 

10,3 Kinds of Error 

10.3.1 Errors may be classified as random or 
systematic, the former affecting the reproducibility 
(precision) of measurement and the latter affecting its 
true accuracy. 



IS 14673 : 1999 



10.3.2 The standard deviation of a set of n 
measurements of a quantity Kunder steady conditions 
may be estimated from the equation: 



sr = 






^1/2 



where Y is the arithmetic mean ofthe/i measurements. 
Tne standard deviation of the mean is then given by: 



Sy 



and the uncertainty of the mean is twice s^ (to 95 
percent confidence level)**. This uncertainty is the 
contribution of the observations of Y to the total 
uncertainty. 

10,3.3 A measurement may also be subject to 
systematic error; the mean of very many measured 
values would thus still differ from the true value of 
the quantity being measured. An error in setting the 
zero of a water level gauge to invert level, for 
example, produces a systematic difference between 
the true mean measured head and the actual value. 
As repetition of the measurement does not eliminate 
systematic errors, the actual value could only be 
determined by an independent measurement known 
to be more accurate. 

10.4 Errors in Coefficient Value 

10.4.1 The values of the discharge coefficients C^ 
and C^ quoted in this standard are based on an 
appraisal of experim.ents, which may be presumed 
to have been carefully carried out, with sufficient 
repetition of the readings to ensure adequate 
precision. Random and systematic errors from this 
source are small, However, when measurements are 
made on other similar installations, systematic 
discrepancies between coefficients of discharge may 
well occur, which may be attributed to variations in 
the surface finish of the device, its installation, the 
approach conditions, the scale effect between model 
and site structure, etc. 

10.4.2 The uncertainty in the coefficients quoted 
in the preceding clauses of this standard are based 
on a consideration of the deviation of experimental 
data from various sources from the equations 
given. The suggested uncertainties thus represent 
the accumulation of evidence and experience 
available. 

'* This factor of two assumes that n is large, for « = 6, the factor should 
be 2.6; /I -8 requires 2,4; n = 10 requires 2.3; « = 15 requires 2.1, 



10.5 Uncertainties in Measurements Made by the User 

10.5.1 Beth random and systematic errors will occur 
in measurements made by the user. 

10.5.2 Since neither the method of measurement nor 
the way in which they are to be made are specified, no 
numerical values can be suggested for uncertainties 
in this category; they shall be estimated by the user. 
For example, consideration of the method of measuring 
the weir width should permit the user to estimate the 
uncertainty in this quantity. 

10.5.3 The uncertainty in the gauged head shall be 
determined fi^om an assessment of the separate sources 
of uncertainty, for example, the uncertainty of the zero 
setting, wind set-up, the gauge sensitivity, backlash 
in the indicating equipment (where appropriate), the 
residual uncertainty in the mean of a series of 
measurements (where appropriate). 

10.6 Combination of Uncertainties 

10.6.1 The total systematic or random uncertainty is 
the resultant of several contributory uncertainties, which 
may themselves be composite uncertainties. Provided 
the contributing uncertainties are independent, small 
and numerous, they may be combined together to give 
overall a random (or systematic) uncertainty at the 95 
percent confidence level. 

10.6.2 All sources contributing imcertainties will have 
both random, and system.atic com^ponents. However, 
in some cases either the random or the systematic 
component may be predominant and the other 
component can be neglected by comparison. 

10.6.3 Because of the different na^are of random and 
systematic uncertainties, they should not normally be 
combined with each other. However, with the 
provisions of 10.6.1 random uncertainties from 
different sources may be combined together by the root- 
sum of squares rule; systematic uncertainties from 
different sources may be similarly combined. 

10.6.4 The percentage random uncertainty A* in the rate 
of flow m.ay be calculated from, the following equation: 



Xij=±4xfir^^+^^^ 



where 



X' ^ the percentage random uncertainty in 

X'^ ^ the percentage random uncertainty in 6; 
X'^^ = the percentage random uncertainty in h. 

In the above, A^^ == lOOx^ 
b 

and X{,^(,Xl,' + ,Xi,'+ + X-^f 



IS 14673 : 1999 



where 



1 ^h' » 2^h' 



x^ 



the random uncertainty in breadth 
measurement; 

etc, are percentage random 

uncertainties in head measurement 
{see 10.5.3); and 

the percentage random uncertainty of 
the mean if a series of readings of 
head measurement are taken at 
constant water level. 

The term^^ is easily estimated if, for example, a point 
gauge is used for water level measurement. For 
continuous or digital recording equipment, the random 
uncertainty in reading a given water level can be 
assessed by laboratory tests on the equipment. 

10.6.5 The percentage systematic uncertainty X"' in 
the rate of flow may be calculated from the foUowmg 
equatidh: 



X\ - ±V^"^^X"g + 1.5^X' 



where 



X" = the percentage systematic uncertainty in 

X*'^ == the percentage systematic uncertainty in b\ 
X'\ = the percentage systematic uncertainty in h; 

In the above X\ = (,X"^ + 2^i + f^ 

where ivt'*h>2^*h ^^^' ^^^ percentage systematic 
uncertainties in head measurement {see 10.5.3). 

10.7 Presentation of Results 

10.7.1 Although it is desirable, and frequently 
necessary, to list total random and total systematic 
uncertainties separately, it is appreciated that simpler 
presentation of results may be required. 

For the purpose, random and systematic uncertainties 
may be combined as shown in ISO 5168 



Xg^±p(^^HX^' 



11 EXAMPLES 

1 LI Example 1 

The following is an example of the computation of 
the flow rate and associated uncertainty in a single 
measurement of flow using a triangular profile weir, 
for modular flow conditions. The crest height;? above 



the bed of the approach channel is 1 m and the gauged 
head h is 0.67 m. The breadth of the weir crest b and 
the breadth of the approach channel B are both equal 
to 10 m. 

11.1.1 For calculation of the discharge, the equation 
in 9.1.2 is used. Since the guaged head h is greater 
than 0. 1 m, C^ = 1 . 1 63 . For modular flow the drowned 
flow reduction factor equals 1. 

1L1*2 In order to read C^ from Fig. 2, it is necessary 
to evaluate 2/3 ^JlThC^bhf A where A is the cross- 
sectional area of flow in the approach channel, in this 
case equal to B {h-^p) or 10 (0.67 + 1) = 16.7 m^ 

Then 

2/3 V273Q6/i/ ^ = 2/37273x1.163x10x0.67/ 16.7 
= 0.254 

With this value, from Fig. 2, C - 1,054. 
11.1.3 Using the equation in 9.1.2: 



Q={2/3f^C,C,f^bh 



3/2 



x3/2 



3/2 



=(2/3)'''^xl.l63xL054xlxV9.81xl0x(0.67) 
= 11.46m^/s. 

1LL4 To calculate the uncertainty in this value of ^, 
the uncertainties in the coefficient values are first 
determined: 



(from 9.4) 

(from 9.4) 



X'^ =±0.5 percent 

^ pO..I.054 ^ 

- ±1.54 percent 

11.1.5 Assuming that several measurements of breadth 
are taken, the random component of uncertainty in 
width measurement is likely to be negligible. The 
systematic uncertainty in length measurement is 
assumed in this case to be O.O-l m. Accordingly, 

X^^O 

Xi;^ — x 100= ±0.1 percent 

11.1.6 With the equipment used it had been 
demonstrated that the gauge zero could be set to within 
±3 mm. This is a systematic uncertainty; however the 
magnitude of the uncertainty shall be related to the 



IS 14673 : 1999 



equipment used. There is no random uncertainty 
associated with the zero setting error, because, until 
the zero is reset the true zero will have the same 
magnitude and sign. Therefore, 



l^H=0 



xi; = 



\^h 



0.003 
0.67 



X 100^ 0.45 percent 



11.L7 Uncertainties associated with different types of 
water level observations equipment can be determined 
by careful tests under controlled conditions. The random 
component of uncertainty can be determined by carrying 
out a series of readings at a given water level; however, 
in order to distinguish the random uncertainty from 
other sources of uncertainty it is necessary that these 
tests should be carried out with the water level always 
rising (or falling). For the equipment used the random 
component of uncertainty in water level measurement 
was approximately ±1 mm. Systematic uncertainties in 
water level measurement occur due to backlash, tape 
stretching, etc. Where possible, corrections should be 
applied, but controlled tests for given types of equipment 
will indicate the magnitude of the residual systematic 
uncertainty. In the present case this was approximately 
±2.5 mm. Accordingly 



X'^ = ^^^x 100 = O.lSpercent 



2^ h 



X'l^± 



0.67 
0.0025 



2-^ h 



0.67 



xlOO = 0.37 percent 



11. L8 The combination of individual uncertainties to 
obtain the overall uncertainty in discharge may be 
carried out as follows: 

The uncertainties in water level measurement are 
assuming X'^ is negligible: 



Xh-^S \Xh + 2^h 

= ± ^/o + ol? = ± O.l 5 percent 

x;; = ±yl,x'f;'^2^f 

= ±^0.45^ +0.37^ =±0.58 percent 
Total random uncertainty in discharge measurement: 

xl/2 



X^=±{x^'+Xi'^l5'X{,') 

-±(0.5^+0 + 2.25x0.15^) 
= ±0,55 percent. 



1/2 



Total systematic uncertainty in discharge 
measurement: 



X'q =±{X'l +^'^ + 1.5^ X{:^f^ 

= ±(1.54^+0.1^+2.25x0.58^)*^^ 
= ±1.77 percent. 

In order to facilitate a simple presentation, the random 
and systematic uncertainties may be combined by the 
root-sum of squares rule 

Xq = ±7oi?+l77^ = ±1.85 percent 

The flow rate Q may be reported as 

1 1 .46 mVs ± 1 .85 percent; Random uncertainty = ±0.55 
percent. 

11.2 Example 2 

The following is an example of the computation of 
the flow rate and associated uncertainty in a single 
measurement of flow using a triangular profile weir, 
for drowned flow conditions. The crest height p is 
1 m, and the gauged height h is 2.2 m. The crest 
tapping head h is 1 .7 m. The breadth of weir crest b 
and the breadth of the approach channel B are both 
equal to 10 m. The same digital punched type recorder 
is assumed as in the previous example. 

1 1.2.1 Since the gauged head h is greater than 0. 1 m, 
C - 1.163. 

d 

11.2.2 In order to read C^from Fig. 3, it is necessary 
to evaluate llZ^inC^bhl A and h Ik 

A - 10(2.2+ l)-32m^ 

Then 

2/3 V273Q^/(/ ^ = 2/ 3V27Ix 1.163x10x2.2/32 
= 0.436 

Also, /iZ/i - 1.7/2.2 = 0.773 
Then, from Fig. 3, C/- 0.88. 

11.2.3 Using the equation in 9.1.2 



Q--{2/3f^C,^Cj4ghh 



3/2 



.3/2 



e = (2/3)'^" xl.l63x0.88V9.81x 10x2.2 
= 56.94 m^/s 



3/2 



10 



IS 14673 : 1999 



11.2.4 The uncertainities in the coefficient values are 
calculated as follows: 

X^ =^± 0.5 percent (from 9.4) 

Referring to Table i, with h Ih ^ 0.113 and 

in^imc^hhl A = 0.436, by interpolation 

xl = ±7.6 percent approximately. 

11.2.5 As in the previous example, 

4-0 

X^= ±0.1 percent. 

11.2.6 Assuming that the gauge zero could be set to 
within ± 3 mm: 

J X'^ = +£:5^ x\m^ ± 0.14 percent 

11.2.7 Using the same uncertainties associated 
with the water level equipment as in the pcvious 
example. 



2^h 



-> xi: 



0.001 

2.2 

0-002 5 



xlOO - ±0.045 percent 



xlOO^ ±0.1 I percent 



11.2.8 The resulting uncerTainties it' '.vatcr level 
measurement arc, assuming A",^, is negligible. 



X{^^±^^Xl^+ 2^A^ - ±^0 + 0.045^ 
= ±0.05 percent 



X^^±^^Xf^ 2^A^ = ±^0.14^0.11^ 
= ±0.1 8 percent 

Total random uncertainty in discharge measurement 

-±(0.5^+0 + 2.25x0.05^) 
= ±0.51 percent 
Total systematic uncertainty in discharge measurement 



1'2 



1/2 



X'^^±(xf^x;^'^Wxf] 

= ±(7.6^+0.1^+2:25x0.18^) 
= ±7.61 percent 



For simplicity of presentation, the random and 
systematic components of uncertainty may be combmed: 

Xq =±^0.51- +7.61- = ±7.63 percent 

The flow rate may be reported as: 

56.94mVs±7 63 percent; 

Random uncertainty = ± 0.51 percent, 



II 



IS 14673 : 1999 



ANNEX A 
{Clause 3) 
SYMBOLS 



Symbol 


Designation 


Units of 
Measurement 


A 


area of approach channel 


m^ 


B 


breadth of approach channel 


m 


b 


breadth of weir crest 


m 


Ci 


coefficient of discharge 


non-dimensional 


Cv 


coefficient of approach velocity 


non-dimensional 


/ 


drowned flow reduction factor 


non-dimensional 


g 


acceleration due to gravity 


m/s^ 


H 


total (energy) head above crest level 


m 


h,hi 


upstream gauged head above crest level 


m 


h2 


downstream gauged head above crest level 


m 


K 


measured crest tapping head above crest level 


m 


n 


number of measurement in a set 


— 


P 


height of weir (difference between mean bed level and crest level) 


m 


Q 


total discharge 


mVs 


■sy 


standard deviaton of a quantity Y 


~ 


'y 


standard deviaton of the mean 


— 


X 


over percentage uncertainty 


% 


^b 


percentage uncertainty in h 


% 


Xc 


percentage uncertainty in Cd C^f 


% 


x^ 


percentage uncertainty in h 


% 


■^m 


percentage uncertainty in the mean of a set of head measurement readings 


% 


^0 


percentage uncertainty in Q 


% 


b 


random uncertainty in breadth measurement 


m 


Superscrif 


>ts to X : ' denotes random components of uncertainty 

" denotes systematic components of uncertainty 





12 



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Date of Issue 



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